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Update Content - 2024-12-17

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Thomas Dehaeze
2024-12-17 15:37:17 +01:00
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content/book/morrison16_groun_shiel.md
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@@ -148,7 +148,7 @@ In a few elements, the atomic structure is such that atoms align to generate a n
The flow of electrons is another way to generate a magnetic field.
The letter \\(H\\) is reserved for the magnetic field generated by a current.
Figure [6](#figure--fig:morrison16-H-field) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
[Figure 6](#figure--fig:morrison16-H-field) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
<a id="figure--fig:morrison16-H-field"></a>
@@ -167,7 +167,7 @@ Ampere's law states that the integral of the \\(H\\) field intensity in a closed
\boxed{\oint H dl = I}
\end{equation}
The simplest path to use for this integration is the one of the concentric circles in Figure [6](#figure--fig:morrison16-H-field), where \\(H\\) is constant and \\(r\\) is the distance from the conductor.
The simplest path to use for this integration is the one of the concentric circles in [Figure 6](#figure--fig:morrison16-H-field), where \\(H\\) is constant and \\(r\\) is the distance from the conductor.
Solving for \\(H\\), we obtain
\begin{equation}
@@ -179,7 +179,7 @@ And we see that \\(H\\) has units of amperes per meter.
### The solenoid {#the-solenoid}
The magnetic field of a solenoid is shown in Figure [7](#figure--fig:morrison16-solenoid).
The magnetic field of a solenoid is shown in [Figure 7](#figure--fig:morrison16-solenoid).
The field intensity inside the solenoid is nearly constant, while outside its intensity falls of rapidly.
Using Ampere's law <eq:ampere_law>:
@@ -196,7 +196,7 @@ Using Ampere's law <eq:ampere_law>:
### Faraday's law and the induction field {#faraday-s-law-and-the-induction-field}
When a conducting coil is moved through a magnetic field, a voltage appears at the open ends of the coil.
This is illustrated in Figure [8](#figure--fig:morrison16-voltage-moving-coil).
This is illustrated in [Figure 8](#figure--fig:morrison16-voltage-moving-coil).
The voltage depends on the number of turns in the coil and the rate at which the flux is changing.
<a id="figure--fig:morrison16-voltage-moving-coil"></a>
@@ -236,7 +236,7 @@ The unit of inductance if the henry.
</div>
For the coil in Figure [7](#figure--fig:morrison16-solenoid):
For the coil in [Figure 7](#figure--fig:morrison16-solenoid):
\begin{equation} \label{eq:inductance\_coil}
V = n^2 A k \mu\_0 \frac{dI}{dt} = L \frac{dI}{dt}
@@ -476,21 +476,21 @@ For example, signals that overload an input stage can produce noise that may loo
### The basic shield enclosure {#the-basic-shield-enclosure}
Consider the simple amplifier circuit shown in Figure [9](#figure--fig:morrison16-parasitic-capacitance-amp) with:
Consider the simple amplifier circuit shown in [Figure 9](#figure--fig:morrison16-parasitic-capacitance-amp) with:
- \\(V\_1\\) the input lead
- \\(V\_2\\) the output lead
- \\(V\_3\\) the conducting enclosure which is floating and taken as the reference conductor
- \\(V\_4\\) a signal common or reference conductor
Every conductor pair has a mutual capacitance, which are shown in Figure [9](#figure--fig:morrison16-parasitic-capacitance-amp) (b).
The equivalent circuit is shown in Figure [9](#figure--fig:morrison16-parasitic-capacitance-amp) (c) and it is apparent that there is some feedback from the output to the input or the amplifier.
Every conductor pair has a mutual capacitance, which are shown in [Figure 9](#figure--fig:morrison16-parasitic-capacitance-amp) (b).
The equivalent circuit is shown in [Figure 9](#figure--fig:morrison16-parasitic-capacitance-amp) (c) and it is apparent that there is some feedback from the output to the input or the amplifier.
<a id="figure--fig:morrison16-parasitic-capacitance-amp"></a>
{{< figure src="/ox-hugo/morrison16_parasitic_capacitance_amp.svg" caption="<span class=\"figure-number\">Figure 9: </span>Parasitic capacitances in a simple circuit. (a) Field lines in a circuit. (b) Mutual capacitance diagram. (b) Circuit representation" >}}
It is common practice in analog design to connect the enclosure to circuit common (Figure [10](#figure--fig:morrison16-grounding-shield-amp)).
It is common practice in analog design to connect the enclosure to circuit common ([Figure 10](#figure--fig:morrison16-grounding-shield-amp)).
When this connection is made, the feedback is removed and the enclosure no longer couples signals into the feedback structure.
The conductive enclosure is called a **shield**.
Connecting the signal common to the conductive enclosure is called "**grounding the shield**".
@@ -502,13 +502,13 @@ This "grounding" usually removed "hum" from the circuit.
Most practical circuits provide connections to external points.
To see the effect of making a _single_ external connection, open the conductive enclosure and connect the input circuit common to an external ground.
Figure [11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (a) shows this grounded connection surrounded by an extension of the enclosure called the _cable shield_.
[Figure 11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (a) shows this grounded connection surrounded by an extension of the enclosure called the _cable shield_.
A problem can be caused by an incorrect location of the connection between the cable shield and the enclosure.
In Figure [11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (a), the electromagnetic field in the area induces a voltage in the loop and a resulting current to flow in conductor (1)-(2).
In [Figure 11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (a), the electromagnetic field in the area induces a voltage in the loop and a resulting current to flow in conductor (1)-(2).
This conductor being the common ground that might have a resistance \\(R\\) or \\(1\\,\Omega\\), this current induced voltage that it added to the transmitted signal.
Our goal in this chapter is to find ways of keeping interference currents from flowing in any input signal conductor.
To remove this coupling, the shield connection to circuit common must be made at the point, where the circuit common connects to the external ground.
This connection is shown in Figure [11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (b).
This connection is shown in [Figure 11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (b).
This connection keeps the circulation of interference current on the outside of the shield.
There is only one point of zero signal potential external to the enclosure and that is where the signal common connects to an external hardware ground.
@@ -655,7 +655,7 @@ If the resistors are replaced by capacitors, the gain is the ratio of reactances
This feedback circuit is called a **charge converter**.
The charge on the input capacitor is transferred to the feedback capacitor.
If the feedback capacitor is smaller than the transducer capacitance by a factor of 100, then the voltage across the feedback capacitor will be 100 times greater than the open-circuit transducer voltage.
This feedback arrangement is shown in Figure [17](#figure--fig:morrison16-charge-amplifier).
This feedback arrangement is shown in [Figure 17](#figure--fig:morrison16-charge-amplifier).
The open-circuit input signal voltage is \\(Q/C\_T\\).
The output voltage is \\(Q/C\_{FB}\\).
The voltage gain is therefore \\(C\_T/C\_{FB}\\).